Since the concurrence, one of the bipartite entanglement measure, is defined as \({\cal C} = 2 |a_{00} a_{11} - a_{01} a_{10}|\)  for two qubit pure state \(\vert \psi  \rangle  = \sum _{i,j=0}^1 a_{ij} \vert ij \rangle \)  [1]}, [2]},
\(U_{\mbox{oracle}}\)  changes the separable state \(\vert s \rangle \)  into the maximally entangled state \(\vert \psi _{\mbox{oracle}} \rangle \) . Then, \(U_{\mbox{diffuser}}\)  exactly detects \(\vert \psi _G \rangle \) , which means
\(U_{\mbox{diffuser}} \vert \psi _{\mbox{oracle}} \rangle  = \vert \psi _G \rangle \) .
Therefore, \(U_{\mbox{oracle}}\)  creates an entanglement maximally and \(U_{\mbox{diffuser}}\)  increases the probability amplitude of \(\vert \psi _G \rangle \)  maximally at the price of complete annihilation of entanglement.
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